The deputy prime minister Nick Clegg has intervened in the row over News Corporation's bid to take over BSkyB to make a direct appeal to Rupert Murdoch to "do the decent thing" and drop the deal.

He said Murdoch should look at the public revulsion towards allegations about phone hacking, payments to police and an "industrial scale" cover-up at News International and reconsider his bid.

It came after the deputy prime minister met the family of murdered teenager Milly Dowler, whose phone was allegedly hacked by the News of the World. The Dowler family's lawyer, Mark Lewis, also called on Rebekah Brooks, chief executive of News International, to "do the honourable thing" and quit.

Clegg told the BBC: "On the BSkyB bid, Rupert Murdoch is now in town in London seeking to sort things out. I would simply say to him, look how people feel about this. Look at how the country has reacted with revulsion to the revelations.

"So do the decent and sensible thing and reconsider: think again about your bid for BSkyB.

"Listening to Bob, Sally and Gemma Dowler, it reminds you that it is innocent families like them who have paid a very heavy price for truly grotesque journalistic practices, which are simply beneath contempt. We owe it to the Dowlers and other innocent victims of hacking to get these inquiries right, to make sure they are really strong, [so] they can get to the bottom of what happened and make sure it never happens again."

The dramatic intervention came as the government scrambled to solve the conundrum of how to delay or even veto the media magnate's bid to gain 100% of BSkyB without facing legal action.

Jeremy Hunt, the culture secretary, on Monday wrote to the media regulator Ofcom asking it to examine the recent revelations to see if they have any bearing on whether the Murdochs are "fit and proper" people to hold large broadcasting licences in the UK.

Labour is threatening a Commons vote on Wednesday on the issue, which would not be legally binding but would make it almost impossible for the government not to act. Several senior Lib Dems have indicated that they could back such a vote if it is not too partisan.

Clegg was speaking after a 50-minute meeting with the Dowler family to discuss their views on how the two inquiries the government is instigating should be carried out.

The mother, father and sister of Milly Dowler – whose phone was allegedly hacked by investigators working for the News of the World in the days after she went missing – pushed Clegg to hold broad inquiries, not just restricted to the practices at the News of the World or the allegations of press payments to the Metropolitan police, but to other forces as well.

Speaking from the steps of the cabinet office, the Dowler family's lawyer Mark Lewis said his clients "take the view that Rebekah Brooks should do the honourable thing".

"They don't see why she should stay in the job. They see this as something that went right to the top. She was editor of the News of the World at the time that Milly was taken in 2002. She should take editorial responsibility."

The former Scotland Yard deputy assistant commissioner Brian Paddick, who was also hacked and also attended the meeting, said Surrey police should have told the Dowler family that they may have been targeted.

He told the press conference: "Apparently Surrey police knew at the time that the phone was being hacked into. Why they didn't tell the family at all … is a matter for Surrey police to answer. What it does show is that this relationship between the police and the press is not restricted to the Metropolitan police."